A simple graph G = (V,E) admits an H-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs H ′ of G isomorphic to H , the H ′-weights, wtf(H ′) = ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e), form an arithm...

Image segmentation has many applications which range from machine learning to medical diagnosis. In this paper, we propose a framework for the segmentation of images based on super-pixels and algorithms for community identification in graphs. The super-pixel presegmentation step reduces the number of nodes in the graph, rendering the method the ability to process large images. Moreover, communi...

The super edge-connectivity λ′ of a connected graph G is the minimum cardinality of an edge-cut F in G such that every component of G − F contains at least two vertices. LetGi be a connected graph with order ni , minimum degree δi and edge-connectivity λi for i = 1, 2. This article shows that λ′(G1 × G2) ≥ min{n1 λ2,n2 λ1,λ1 + 2λ2, 2λ1+λ2} forn1,n2 ≥ 3 andλ′(K2×G2) = min{n2, 2λ2}, which general...

A k-container C(u, v) of G between u and v is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k∗-container if it contains all nodes of G. A graph G is k∗connected if there exists a k∗-container between any two distinct nodes. The spanning connectivity of G, κ∗(G), is defined to be the largest integer k such that G is w∗-connected for all 1 ≤ w ≤ k if G is a...

Let [Formula: see text] be a simple graph. A dominating set of is subset such that every vertex not in adjacent to at least one text]. The cardinality smallest text], denoted by the domination number called super if for there exists In this paper, we study some graph classes and present sharp bounds operations.

This paper presents a new and efficient algorithm, ILIGRA, for inverse line graph construction. Given a line graph H , ILIGRA constructs its root graph G with the time complexity being linear in the number of nodes in H . If ILIGRA does not know whether the given graph H is a line graph, it firstly assumes that H is a line graph and starts its root graph construction. During the root graph cons...

We obtain the existence of a cohomological obstruction to expressing N = 2 line bundles as tensor products of N = 1 bundles. The motivation behind this paper is an attempt at understanding the N = 2 super KP equation via Baker functions, which are special sections of line bundles on supercurves. There has been—for some time now (cf. [DG])—an interest in extending the study of the super KP equat...